@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-ZGXZNMZ8-L
  skos:broader psr:-RN57KZJ9-9, psr:-VTR5XXB2-M ;
  skos:definition """In mathematics, <b>Euler's identity</b> (also known as <b>Euler's equation</b>) is the equality
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle e^{i\\\\pi }+1=0}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>e</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>i</mi>
<br/>            <mi>π<!-- π --></mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>+</mo>
<br/>        <mn>1</mn>
<br/>        <mo>=</mo>
<br/>        <mn>0</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle e^{i\\\\pi }+1=0}</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7464809a40f9e486de3a454745f572fbf8bb256" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -0.505ex; width:11.089ex; height:2.843ex;" alt="{\\\\displaystyle e^{i\\\\pi }+1=0}"></div>
<br/>where
<br/>
<br/><dl><dd><span class="texhtml mvar" style="font-style:italic;">e</span> is Euler's number, the base of natural logarithms,</dd>
<br/><dd><span class="texhtml mvar" style="font-style:italic;">i</span> is the imaginary unit, which by definition satisfies <span class="texhtml"><i>i</i><sup>2</sup> = −1</span>, and</dd>
<br/><dd><span class="texhtml mvar" style="font-style:italic;">π</span> is pi, the ratio of the circumference of a circle to its diameter.</dd> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Euler%27s_identity">https://en.wikipedia.org/wiki/Euler%27s_identity</a>)"""@en, """En mathématiques, l'<b>identité d'Euler</b> est une relation entre plusieurs constantes fondamentales et utilisant les trois opérations arithmétiques d'addition, multiplication et exponentiation&nbsp;:
<br/>
<br/><center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathrm {e} ^{\\\\mathrm {i} \\\\pi }+1=0}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">e</mi>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mi mathvariant="normal">i</mi>
<br/>            </mrow>
<br/>            <mi>π<!-- π --></mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>+</mo>
<br/>        <mn>1</mn>
<br/>        <mo>=</mo>
<br/>        <mn>0</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {e} ^{\\\\mathrm {i} \\\\pi }+1=0}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2bca7543787faa55f2781b4d3df77aaed2a7fdb" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:10.928ex; height:2.843ex;" alt="{\\\\displaystyle \\\\mathrm {e} ^{\\\\mathrm {i} \\\\pi }+1=0}"></span></center>
<br/>où la base <span class="texhtml">e</span> du logarithme naturel représente l'analyse, l'unité imaginaire <span class="texhtml">i</span> représente l'algèbre, la constante d'Archimède <span class="texhtml">π</span> représente la géométrie, <span class="need_ref" title="Une source est souhaitée pour ce passage (demandé le janvier 2015)." style="cursor:help;">l'entier 1 l'arithmétique et le <span class="nowrap">nombre 0</span> les mathématiques</span> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Identit%C3%A9_d%27Euler">https://fr.wikipedia.org/wiki/Identit%C3%A9_d%27Euler</a>)"""@fr ;
  skos:inScheme psr: ;
  skos:prefLabel "identité d'Euler"@fr, "Euler's identity"@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Identit%C3%A9_d%27Euler>, <https://en.wikipedia.org/wiki/Euler%27s_identity> ;
  dc:created "2023-07-13"^^xsd:date ;
  dc:modified "2023-07-13"^^xsd:date ;
  a skos:Concept .

psr:-VTR5XXB2-M
  skos:prefLabel "identité"@fr, "identity"@en ;
  a skos:Concept ;
  skos:narrower psr:-ZGXZNMZ8-L .

psr:-RN57KZJ9-9
  skos:prefLabel "analyse complexe"@fr, "complex analysis"@en ;
  a skos:Concept ;
  skos:narrower psr:-ZGXZNMZ8-L .